Details

sample125.0ms

Algorithm

intervals

Results

19.0ms	33×	body	2560	valid
17.0ms	181×	body	80	valid
13.0ms	27×	body	1280	valid
8.0ms	92×	body	80	nan
5.0ms	13×	body	640	valid
3.0ms	4×	body	5120	valid
2.0ms	9×	body	320	valid
1.0ms	6×	body	160	valid

simplify109.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	14	17
1	24	17
2	44	16
3	78	16
4	102	16
5	111	16
done	111	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.9b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.6b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

123.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms	(- (* b b) (* 4.0 (* a c)))
43.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
19.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series451.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
58.0ms	(- (* b b) (* 4.0 (* a c)))
153.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
98.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.1s

Counts

82 → 82

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	152	1565
1	419	1461
2	1725	1245
done	5001	1239

prune380.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.2b

localize38.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
9.2b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
23.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite319.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
84×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-rgt-neg-in`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 154

Calls

4 calls:

51.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
134.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
100.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
19.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series734.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
217.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
280.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
124.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.3s

Counts

166 → 166

Iterations

Useful iterations: 2 (716.0ms)

Iter	Nodes	Cost
0	253	5113
1	659	4543
2	3723	4219
done	5000	4219

prune641.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.1b

localize19.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0b	(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 4.0 (* a c)))) (* 2.0 a))
9.5b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 4.0 (* a c)))
23.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite401.0ms

Algorithm

rewrite-expression-head

Rules

153×	`times-frac`
122×	`add-exp-log`
80×	`add-sqr-sqrt`
79×	`*-un-lft-identity`
63×	`div-exp`
58×	`add-cbrt-cube`
45×	`associate-/l*`
43×	`add-cube-cbrt`
34×	`prod-exp`
27×	`cbrt-undiv`
18×	`distribute-lft-out--` `difference-of-squares`
14×	`cbrt-unprod`
12×	`sqrt-prod`
10×	`div-inv`
9×	`distribute-rgt-neg-in`
8×	`rec-exp` `1-exp` `add-log-exp`
5×	`pow1`
3×	`flip3--` `flip--` `associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `clear-num` `associate-/r*` `associate-/r/`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-sub` `neg-log`

Counts

4 → 191

Calls

4 calls:

25.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
187.0ms	(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 4.0 (* a c)))) (* 2.0 a))
154.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 4.0 (* a c)))
17.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series655.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
239.0ms	(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 4.0 (* a c)))) (* 2.0 a))
163.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 4.0 (* a c)))
117.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify691.0ms

Counts

203 → 203

Iterations

Useful iterations: done (677.0ms)

Iter	Nodes	Cost
0	391	6142
1	1150	5737
done	5000	5014

prune550.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.1b

localize34.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.6b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
23.9b	(sqrt (- (* b b) (* 4.0 (* a c))))
23.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`sqrt-prod` `add-log-exp`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `difference-of-squares`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

49.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
73.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
10.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series473.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
115.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
125.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
104.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.4s

Counts

72 → 72

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	80	1248
1	198	1112
2	777	1036
3	4380	1028
done	5001	1018

prune376.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.1b

regimes316.0ms

Accuracy

86.3% (3.8b remaining)

Error of 9.2b against oracle of 5.4b and baseline of 32.9b

bsearch205.0ms

Steps

Iters	Range		Point
2	2.9557653966214617e-29	3.491579857798755e-29	3.4246030501515935e-29
9	6.995428276738912e-281	4.047248354420239e-273	6.7128383300107e-280
8	-1.2658565361216573e+102	-2.0194296793555897e+99	-6.953668671676068e+101

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	82
1	46	82
done	46	82

end0.0ms

sample3.4s

Algorithm

intervals

Results

771.0ms	848×	body	1280	valid
707.0ms	5893×	body	80	valid
649.0ms	1092×	body	2560	valid
311.0ms	3047×	body	80	nan
171.0ms	463×	body	640	valid
52.0ms	96×	body	5120	valid
48.0ms	235×	body	320	valid
18.0ms	105×	body	160	valid